Question

Tim needs a new car while he attends college in the United States for the next three years. The car he would like has an MSRP of $15,000. A local dealer can get him a three-year loan with a 7% interest rate if Tim can make a $1,500 down payment.

The same dealer offers the same car for lease with a money factor of 0.00271 and a residual value of 75%. The lease requires an additional fee of $1,250 to cover Tim's security deposit and the acquisition and documentation fees for the car.

Tim is looking to drive the car home with the smallest monthly payment. Which of the following statements is true?
a.
The monthly payment for the loan is lower.
b.
The monthly payment for the lease is lower.
c.
The monthly payments for the lease and loan are the same.
d.
You cannot compare the monthly payments for leases and loans.


Please select the best answer from the choices provided.

A
B
C
D

Answer 1

B

Loan payment: monthly rate = 0.07/12, loan = 15000 − 1500 = $13,500, n = 36
Payment ≈ 13500*(0.07/12)/(1−(1+0.07/12)^(−36)) ≈ $416/month.

Lease payment (money factor method): residual = 0.75·15000 = $11,250.
Depreciation = (15000 − 11250)/36 ≈ $104.17/month.
Rent charge = (15000 + 11250)·0.00271 ≈ $71.14/month.
Lease payment ≈ $104.17 + $71.14 ≈ $175.30/month (the $1,250 fee is paid up front).

Thus the lease monthly payment is lower.